I have a system of non-linear DAE and I noticed that the system does not converge if some of the equations are not differentiated. For example, if the control volume equation is represented as this:
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I have implemented a finite volume scheme using Lax-Friedrichs flux and using Roe's linearization. I want to compute the order of convergence vs. the space-step $h$.
I have computed a solution with a ...

If there are two overset grids, how do you decide whether convergence is reached or not? What I did was, after interpolating from one grid to another, I check the rms of conservative variables and if ...

I would greatly appreciate it if you could share some reasons the Conjugate Gradient iteration for Ax = b does not converge? My matrix A is symmetric positive definite.
Thank you so much!
Edit with ...

I am applying an iterative method (projected newton) to an optimization problem. Theoretically, the method should converge linearly. I would greatly appreciate it if you could share how should I test ...

I am trying to find the convergence of an infinite series of which I do not have the nth term. Instead of applying the ratio test for the nth term, I divided the first two terms, then the next two and ...

I've coded up a Stokes Flow problem using finite elements and am in the process of verifying that it works. I'm just not sure what convergence rate I should be expecting as I globally refine the mesh.
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I need to solve two point bondary problem for ODE. The solution of the problem itself is very easy. The real issue is that when solving arising non linear system of equations it always converges to ...

Let's say we want to solve $Ax=b$ ($A$ symmetric positive /semi/definite) with the conjugate residual/gradient method. $A$ comes from FEM where the mesh is being refined. The exact solution is $x_*$ ...

It is well known that for certain linear systems Jacobi and Gauss-Seidel iterative methods have the same convergence behavior, e.g. Stein-Rosenberg Theorem. I am wondering if similar results exist for ...

I'm having a problem with multigrid code I wrote. If I solve Laplace's equation in 2D and use more than 5 grid levels, the V-cycles stop converging after a few cycles (see below, convergence factor > ...

I need to numerically determine the convergence order of Euler's method for various step-sizes. I am unsure how to go about doing this.
Here is the question:
Problem statement: $\frac{dy}{dt}=\alpha ...

Suppose I have the following interesting function:
$$ f(x) = \sum_{k\geq1} \frac{\cos k x}{k^2(2-\cos kx)}. $$
It has some unpleasant properties, like its derivative not being continous at rational ...

I have a system of nonlinear equations of which I know it has a single root I am interested in, and has a continuum of roots I am not interested in. I am currently using Newton with line-searching in ...

When you have fine-scale features (e.g. boundary layers) in the solution, its FEM approximation on coarse meshes converge at strange apparent rates. Looking at Cea's lemma, is this behaviour because ...

I have a non-linear equation that converges, and reaches suitable accuracy after around 20 steps, however each step is very expensive to calculate. The series are never quite the same, but they are ...

I've used an explicit finite difference scheme to model the 1D time dependent temperature distribution in a friction weld. I want to now verify the consistency and convergence of my algorithm.
I have ...

Consider a method (e.g., FEM) with variable approximation order $p$. Now, we know that the optimal order of convergence is given by
$$e = C h^{p+1},$$
where $h$ denotes the mesh size and a constant ...

I am a postgraduate student with interest in numerical methods for solving nonlinear systems of equations. I have read some papers that discussed about 'computational order of convergence' for some ...

I am solving 3D time-harmonic Maxwell FDFD problems (which result in huge sparse linear systems) using BiCGStab(l). I have tried out a bunch of different methods and for my specific use case, it seems ...

Based on the variational principle, one might expect that the ground state energy of a density functional theory (DFT) calculation will decrease as the basis set size increases. (As I understand it, ...

I examine the following recursion $X_{n+1}=\frac{t_n}{t_{n+1}}X_n+\frac{Y_n}{t_{n+1}}$ where $X_n,Y_n$ are positive finite random variables and $t_n$ the time. I have shown that $\lim_{n \to \infty} ...

From what I understand the GMRES method is (using Arnoldi Iterations/Modified Gram-Schmidt):
The first vector of the Krylov subspace span of A is the normalized vector $\frac{\vec b - A\vec x_0} {|| ...